I'm totally down for how nifty it would be to have off-world colonies, but trying to sell it to the public with these "what if" arguments doesn't even begin to pass the sniff test. Gates has been sounding the alarm for years about viral pandemics and basically nothing was prepared for it; how capable would we be of spending trillions on a "backup Earth" when we can't even spend a few million a year on stockpiling medical PPE?
Barring a general change in the habitability of the Moon/Mars or other astronomical body I'd wager that you would have a similar dynamic. If unique economic purposes are discovered including rich surface deposits, low-G fuel generation, or lower environmental concerns then the population in these settlements would grow for the same reasons that people have always moved to the frontier.
Once the transit economics are understood, The Moon and Mars can both provide accessible surface deposits of water, iron, copper, and other commodities to orbit for less energy than earth. A number of activities for resource procurement for commercial space industries will be a tad easier when attached to a big low-g rock where an extra green house can simply be dug out. The relative lack of environmental externalities from mining and other activities may be a resource unto itself in the next few decades.
On a longer timeline - Mars could be given a tolerable atmospheric pressure and liquid water for <100 trillion dollars. Barring a change in global growth rates that would be ~3% of annual global GDP by 2120, and .1% by 2220.